28278 + Interview Questions in Maths in Class 12

1.	Let f(x)={{:([x]",",-2lexle-(1)/(2)),(2x^(2)-1",",-(1)/(2)ltxle2):}" and "g(x)=f(\|x\|)+\|f(x)\| [where [x] represents the greatest integer function.] The number of points where g (x) is discontinuous is -
Answer» 1 2 3 4 Answer :B

Discussion

2.	Let f(x)={{:([x]",",-2lexle-(1)/(2)),(2x^(2)-1",",-(1)/(2)ltxle2):}" and "g(x)=f(\|x\|)+\|f(x)\| [where [x] represents the greatest integer function.] The number of points where \|f(x)\| is non -differentiable is -
Answer» 3 4 2 5 Answer :A

Discussion

3.	We take on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2))=1 (a gt b) a point M(x,y) lying in the first quadrant. Show that the sector of the ellipse bonded by its semi-major axis and the focal radius drawn to the point M has an area. S= (ab)/(2) "arc " "cos "(x)/(a). With the aid of this result deduce a formula for computing the area of the entire ellipse.
Answer» ANSWER :`(AB)/(4)PI`

Discussion

4.	For positive l, m and n, if the planes x = my + mz, y =1z+ nx, z=mx+ 1y intersect in a straight, line, then: The equation of the straight line is x/a=y/b=z/c, where the ordered traid (a,b,c) is :
Answer» `sqrt(1-l^(2)) , sqrt(1- m ^(2)), sqrt(1-n ^(2))` 1,m and n `(1)/(sqrt(1-I ^(2))), (m)/(sqrt(1-m^(2)))and (n)/(sqrt(1- n ^(2))` NONE of these ANSWER :A

Discussion

5.	To change (3x+4y+5) - (2x+3y+4)(dy)/(dx) = 0 into homogeneous equation, origin is shifted to (h,k) then h + k = 0
Answer» 3 1 `-2` `-1` ANSWER :D

Discussion

6.	The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 13x^(2) + 26x + 15. Find the marginal revenue when x = 7.
Answer» ANSWER :₹ 208

Discussion

7.	The general solution of the differential equation x^2 y dx - (x^3 + y^3) dy = 0 is
Answer» `y^(3) = 3x^(3) + C` `y^(3) = 3x^(3) log (Cx)` `y^(3) = 3x^(3) + log (Cx)` `y^(3) + 3x^(3) -log(Cx)` ANSWER :B

Discussion

8.	If two fair dice are rolled find the probability that the minimum number on the dice is less than 4.
Answer» ANSWER :`(3)/(4)`

Discussion

9.	There are two circles in xy-plane whose equations are x^(2)+y^(2)-2y=0 and x^(2)+y^(2)-2y-3=0. A point (x,y) is choosen at random inside the larger circle. The the probability that the point has been taken from the smaller circle is
Answer» `1//2` `1//4` `1//6` `1//16` ANSWER :B

Discussion

10.	If tan thea + cot theta =2, then sin thetais equal to
Answer» `(1)/(SQRT2)` `(1)/(SQRT3)` `1/2` `1` ANSWER :A

Discussion

11.	If A(0, 0) and C(6, -8) are end points of diagonal of a square then sum of square of abscissa of other vertex is
Answer» Solution :Using concept of rotation `(x+I y) - (3-4i) = [6-8i-(3-4i)]e^((i PI)/(2))` `x = I y = (3-4i) + (3-4i)i` `rArr x + i y = (3-4i)(1+i)` `x + i y = 3- 4i + 3I + 4` `= 7 - i` x = 7, y = -1 similarly, x = -1, y = -7 `7^(2) + 1^(2) = 50`

Discussion

12.	If (2z_(1))/(3z_(2)) is purely , an imaginary number , then \|(z_(1) - z_(2))/(z_(1) + z_(2))\| is equal to
Answer» `(2)/(3)` `(3)/(2)` `(4)/(9)` 1 Answer :D

Discussion

13.	int_(-1)^(41//2)e^(2x-[2x])dx, where [*] denotes the greatest integer function.
Answer» SOLUTION :N//A

Discussion

14.	int" e"^(sinx).((sinx+1)/(secx))dx is equal to
Answer» `SINX.E^(sinx)+C` `cosx.e^(sinx)+c` `e^(sinx)+c` `e^(sinx)(sinx+1)+c` ANSWER :A

Discussion

15.	A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?
Answer» ANSWER :`(5)/(34)`

Discussion

16.	Two vertices of an equilateral triangle are (0,0) and (3, sqrt(3)) then the third vertex can be
Answer» (`SQRT(3), 3`) `(-3, sqrt(3))` `(3, -sqrt(3))` `(-sqrt(3), 3)` ANSWER :C

Discussion

17.	Let Y = {n^(2) :n in N} subNConsider f: N rarr Yas f(n) = n^2 . Show that f is invertible. Find the inverse of f.
Answer» SOLUTION :N/A

Discussion

18.	Findthe values of lambda and mu so thatthe points A(3,2-4) ,B(9,8,-10)andC(lambda,mu,-6) arecolliinear .
Answer» ANSWER :`lambda=5, mu=4`

Discussion

19.	Let alpha,beta denote the cube roots ofunity other than l and alphaanebeta. Let s=sum_(n=0)^(302)(-1)^(n)((alpha)/(beta))^(n). Then the value of s is
Answer» EITHER -`2OMEGA` or-`2omega^(2)` either `-2omega` or `2omega^(2)` either `2omega` or `-2omega^(2)` either `2omega` or `2omega^(2)` ANSWER :A

Discussion

20.	Choose the correct answer int_(1)^(sqrt3)(dx)/(1+x^(2)) equals
Answer» `pi/3` `(2PI)/3` `pi/6` `pi/12` ANSWER :D

Discussion

21.	Find all points of local maxima and local minima of the function f given by f(x)=x^(3)-3x+3.
Answer» ANSWER :Function has local MAXIMUM VALUE is 1 at X = 1 and local minimum value is 5 at `x=-1`.

Discussion

22.	if sin alpha=3/5 and cos beta=5/13, then the value of cos (alpha-beta) cannot be :-
Answer» `56/65` `10/65` `(-56)/65` `(-16)/65`

Discussion

23.	Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (x+3)^(2). (x+4)^(3). (x+5)^(4).
Answer» ANSWER :`(x+3)(x+4)^(2) (x+5)^(3) (9X^(2)+70x+133)`

Discussion

24.	Find the Principle values of the following : cos^(-1)(-1/2)
Answer» ANSWER :`(2PI)/3`

Discussion

25.	Using differential, find the approximate value of each of the following upto 3 places of decimal.(82)^(1//4)
Answer» SOLUTION :`(82)^(1//4)=3.99`

Discussion

26.	If vec(a)=hati+hatj+2hatk and vec(b)=3hati+2hatj-hatk then find vec(a)+3vec(b).(2vec(a)-vec(b)).
Answer» ANSWER :`-15`

Discussion

27.	Integrate the follwing functions: 1/(x^4-1)
Answer» Solution :`1/(x^4-1) = 1/((x^2-1)(x^2+1))` =`1/2[1/(x^2-1) -1/(x^+1)]` `INT 1/(x^4-1) DX` =`1/2[INT1/(x^2-1) dx -int 1/(x^2+1) dx]` =`1/4 LOG\|(x-1)/(x+1)\| -1/2 tan^-1x +C`

Discussion

28.	IF sintheta=1/2(a+1/a) then the value of sin 30 is
Answer» `1/8(a^3+1/a^3)` `3/2(a+1/a)` `-1/2(a^3+1/a^3)` `1/3(a^3+1/a^3)` ANSWER :C

Discussion

29.	If(1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(4)x^(r ), thena_(r )-""^(n)C_(1)*a_(r-1)+""^(n)C_(2)a_(r-2)- ""^(n)C_(2)a_(r-3)+………+(-1)^(r ) ""^(n)C_(r)a_(0)is equal to : (r is not multiple of 3)
Answer» 0 `""^(N)C_(R)` `a_(r)` 1 Answer :A

Discussion

30.	The point of intersection of the perpendicular bisectors of the sides of the triangle formed by the points (2, 1), (5, 2) and (3, 4) is
Answer» `((13)/(2), (9)/(2))` `((13)/(4), (9)/(4))` `((13)/(2), 3)` `((13)/(5), (9)/(5))` Answer :B

Discussion

31.	Match the column Consider the number = N 123X43Y where x & y are digits 0leXle9and0leyle9. Now answer the following
Answer» `{:("If N is divisible by 2, then the sum of all possible",(p),57):}` `{:("If N is divisible by 3, then the sum of all possiblevale of x+y will be",(Q),17):}` `{:("If N is divisible by 6, then number of orded pairs (x,y) can be",(r),20):}` `{:("If N is divisiable by 9, then the sum of possible value of ",(s),19):}` Answer :A::B::C::D

Discussion

32.	The solution of (1-x^(2)) (dy)/(dx) + xy = xy^(2) is
Answer» `SQRT(x^(2) - 1) = ysqrt(x^(2) +1) + cy` `sqrt(x^(2) - 1) = ysqrt(x^(2) -1) + cy` `sqrt(x^(2) + 1) = ysqrt(x^(2) +1) + cy` `sqrt(x^(2) + 1) = sqrt(x^(2) - 1)+cy` ANSWER :B

Discussion

33.	Find the root common the system of equations log_(10)(3^(x)-2^(4-x))=2+1/4log_(10)16-x/2 log_(10)4 and log_(3) (3x^(2-13x+58)+(2)/(9))=log_(5)(0.2)
Answer» ANSWER :`x=3`

Discussion

34.	Find the antiderivative (or integral) of the following functions by the method of inspection. sin2x
Answer» SOLUTION :`int SIN2X DX = -(COS2X)/2 +c`

Discussion

35.	Manufacturer can sell x items at a price of rupees (5-(x)/(100)) each. The cost price of x items is Rs. ((x)/(5)+500). Find the number of items he should sell to earn maximum prodit.
Answer» ANSWER :240

Discussion

36.	Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.
Answer» ANSWER :`y^(2) - 2XY(DY)/(dx) = 0`

Discussion

37.	If alpha, beta ne 0 and f(n)=a^(n)+beta^(n) and \|(3,1+f(1),1+f(2)),(1+f(1),1+f(2), 1+f(3)),(1+f(2), 1+f(3),1+f(4))\|= K(1-alpha)^(2)(1-beta)^(2)(alpha-beta)^(2), then K is equal to:
Answer» 1 -1 `ALPHA BETA` `1/( alpha beta)` ANSWER :A

Discussion

38.	Find the approximate value of each of the following :log_(e )(100.1)
Answer» ANSWER :`4.6062`

Discussion

39.	int1/(sqrt(3-6x-9x^(2)))dx is equal to
Answer» `sin^(-1)((3x+1)/2)+c` `sin^(-1)((3x+1)/6)+c` `1/3sin^(-1)((3x+1)/2)+c` `sin^(-1)((2x+1)/3)+c` Answer :C

Discussion

40.	int e^(x).(x^(3) + x + 1)/((1 + x^(2))^(3//2)) dx =
Answer» `(E^(x))/(sqrt(1 + x^(2))) + C` `(e^(x) sqrt(1 + x^(2)))/(x ) + c` `e^(x).(x)/(sqrt(1 +x^(2))) + c` `(e^(x).x)/((1 + x^(2))^(3//2)) +c` Answer :C

Discussion

41.	If the normals at two points on the parabola intersects on the curve then the product of the ordinates of the points is
Answer» 8A `8a^(2)` `8a^(3)` `8a^(4)` ANSWER :B

Discussion

42.	Evaluate the following integrals: int (2x+3)/(5x^2+1)
Answer» Solution :`(2X+13/(5x^2+1) = (2x)/(5x^2+1) + 3/(5x^2 +1) ` ` =1/5 (10x)/(5x^2+1) + 3/((sqrt5x)^2 +1)` THEREFORE` int_0^1 (2x+3)/(5x^2+1) dx` =`[1/5 log\|5x^2+1\| +3/sqrt5 tan^-1 (sqrt5x)]_0^1` `(1/5 log6 +3/sqrt5 tan^-1 sqrt5)-(1/5 LOG1 + 3/sqrt5 tan^-1 0)` =`1/5 log6 +3/sqrt5 tan^-1 sqrt5`

Discussion

43.	The sum of the coefficients in the expansion of (1+x-3x^2)^(171) is
Answer» 0 1 `-1` 2 Answer :C

Discussion

44.	Find points of local maxima //minima of (i) f(x) =(2'-1)(2'-2)^(2) (ii) f(x) =x^(2) e^(-x) (iii) f(x) =3cos^(4)x +10cos^(3)x +6cos^(2)x-3,x in [0,pi] (iv) f(x) =2x +3x^(2//3) (v) f(x) =\|(x^(2)-2)/(x^(2)-1)\|
Answer» Answer :(i) localmaxima at `x=log_(2) (4)/(3)` andlocalminima at x=1 (ii) localmin at 0, localmax at 2 (iii) localmax at`x=0 (2pi)/(3),` local MIN at`x=(PI)/(2), pi` (IV) localmaximaat -1and localminma at 0 (v) localminimaat `x=+- SQRT(2) , 0`

Discussion

45.	Tooth which embedded in a bony socket of jaw bone is called :-
Answer» ACRODONT Thecodont Pleurodont Diphyodont Answer :A

Discussion

46.	The ratio in which the plane vec r . (i-2j+3k) =17 divides the line joining the points -2i+4j+7k and 3i-5j+8k is
Answer» `1:5` `1:10` `3:5` `3:10` ANSWER :D

Discussion

47.	Evaluate : int(e^(2x))/(e^(x) + 2) dx
Answer» ANSWER :`e^(X) - 2 LOG \|e^(x) + 2X \| + c`

Discussion

48.	Find the number of 4 digited numbers that can be formed by using the digit 0,2,3,5,7,8 which are divisble by 2
Answer» ANSWER :156

Discussion

49.	A box contains 12 two rupee coins, 7 one rupee coins and 4 half rupee coins. If 3 coins are selected at random, find the probability that (i) sum of three coins is maximum (ii) each coin is of different value (iii) selection contains atleast one rupee coin (iv) all selected 3 coins have same value
Answer» Answer :`(i) (.^(12)C_(3))/(.^(23)C_(3))` `(ii) (12xx7xx4)/(.^(23)C_(3))` `(iii) 1-(.^(16)C_(3))/(.^(23)C_(3))` `(iv) (.^(12)C_(3)+.^(7)C_(3)+.^(4)C_(3))/(.^(23)C_(3))`

Discussion

50.	Integrate the following functions (x^2+1)logx
Answer» Solution :`INT (x^2+1) logx DX` =`logx (x^3/3 +x) -int1/x xx (x^3/3 +x)dx` =`(x^3/3+x) logx-(1/3 x^3/3 +x)+C` =`(x^3/3+x) logx -(x^3/9)-x+c`

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Let f(x)={{:([x]",",-2lexle-(1)/(2)),(2x^(2)-1",",-(1)/(2)ltxle2):}" and "g(x)=f(|x|)+|f(x)| [where [x] represents the greatest integer function.] The number of points where g (x) is discontinuous is -

Let f(x)={{:([x]",",-2lexle-(1)/(2)),(2x^(2)-1",",-(1)/(2)ltxle2):}" and "g(x)=f(|x|)+|f(x)| [where [x] represents the greatest integer function.] The number of points where |f(x)| is non -differentiable is -

For positive l, m and n, if the planes x = my + mz, y =1z+ nx, z=mx+ 1y intersect in a straight, line, then: The equation of the straight line is x/a=y/b=z/c, where the ordered traid (a,b,c) is :

To change (3x+4y+5) - (2x+3y+4)(dy)/(dx) = 0 into homogeneous equation, origin is shifted to (h,k) then h + k = 0

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 13x^(2) + 26x + 15. Find the marginal revenue when x = 7.

The general solution of the differential equation x^2 y dx - (x^3 + y^3) dy = 0 is

If two fair dice are rolled find the probability that the minimum number on the dice is less than 4.

There are two circles in xy-plane whose equations are x^(2)+y^(2)-2y=0 and x^(2)+y^(2)-2y-3=0. A point (x,y) is choosen at random inside the larger circle. The the probability that the point has been taken from the smaller circle is

If tan thea + cot theta =2, then sin thetais equal to

If A(0, 0) and C(6, -8) are end points of diagonal of a square then sum of square of abscissa of other vertex is

If (2z_(1))/(3z_(2)) is purely , an imaginary number , then |(z_(1) - z_(2))/(z_(1) + z_(2))| is equal to

int_(-1)^(41//2)e^(2x-[2x])dx, where [*] denotes the greatest integer function.

int" e"^(sinx).((sinx+1)/(secx))dx is equal to

Two vertices of an equilateral triangle are﻿ (0,0) and (3, sqrt(3)) then the third vertex﻿ can be

Let Y = {n^(2) :n in N} subNConsider f: N rarr Yas f(n) = n^2 . Show that f is invertible. Find the inverse of f.

Findthe values of lambda and mu so thatthe points A(3,2-4) ,B(9,8,-10)andC(lambda,mu,-6) arecolliinear .

Let alpha,beta denote the cube roots ofunity other than l and alphaanebeta. Let s=sum_(n=0)^(302)(-1)^(n)((alpha)/(beta))^(n). Then the value of s is

Choose the correct answer int_(1)^(sqrt3)(dx)/(1+x^(2)) equals

Find all points of local maxima and local minima of the function f given by f(x)=x^(3)-3x+3.

if sin alpha=3/5 and cos beta=5/13, then the value of cos (alpha-beta) cannot be :-

Differentiate the functions given in Exercises 1 to 11 w.r.t. x. (x+3)^(2). (x+4)^(3). (x+5)^(4).

Find the Principle values of the following : cos^(-1)(-1/2)

Using differential, find the approximate value of each of the following upto 3 places of decimal.(82)^(1//4)

If vec(a)=hati+hatj+2hatk and vec(b)=3hati+2hatj-hatk then find vec(a)+3vec(b).(2vec(a)-vec(b)).

Integrate the follwing functions: 1/(x^4-1)

IF sintheta=1/2(a+1/a) then the value of sin 30 is

If(1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(4)x^(r ), thena_(r )-""^(n)C_(1)*a_(r-1)+""^(n)C_(2)a_(r-2)- ""^(n)C_(2)a_(r-3)+………+(-1)^(r ) ""^(n)C_(r)a_(0)is equal to : (r is not multiple of 3)

The point of intersection of the perpendicular bisectors of the sides of the triangle formed by the points (2, 1), (5, 2) and (3, 4) is

Match the column Consider the number = N 123X43Y where x & y are digits 0leXle9and0leyle9. Now answer the following

The solution of (1-x^(2)) (dy)/(dx) + xy = xy^(2) is

Find the root common the system of equations log_(10)(3^(x)-2^(4-x))=2+1/4log_(10)16-x/2 log_(10)4 and log_(3) (3x^(2-13x+58)+(2)/(9))=log_(5)(0.2)

Find the antiderivative (or integral) of the following functions by the method of inspection. sin2x

Manufacturer can sell x items at a price of rupees (5-(x)/(100)) each. The cost price of x items is Rs. ((x)/(5)+500). Find the number of items he should sell to earn maximum prodit.

Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.

If alpha, beta ne 0 and f(n)=a^(n)+beta^(n) and |(3,1+f(1),1+f(2)),(1+f(1),1+f(2), 1+f(3)),(1+f(2), 1+f(3),1+f(4))|= K(1-alpha)^(2)(1-beta)^(2)(alpha-beta)^(2), then K is equal to:

Find the approximate value of each of the following :log_(e )(100.1)

int1/(sqrt(3-6x-9x^(2)))dx is equal to

int e^(x).(x^(3) + x + 1)/((1 + x^(2))^(3//2)) dx =

If the normals at two points on the parabola intersects on the curve then the product of the ordinates of the points is

Evaluate the following integrals: int (2x+3)/(5x^2+1)

The sum of the coefficients in the expansion of (1+x-3x^2)^(171) is

Find points of local maxima //minima of (i) f(x) =(2'-1)(2'-2)^(2) (ii) f(x) =x^(2) e^(-x) (iii) f(x) =3cos^(4)x +10cos^(3)x +6cos^(2)x-3,x in [0,pi] (iv) f(x) =2x +3x^(2//3) (v) f(x) =|(x^(2)-2)/(x^(2)-1)|

Tooth which embedded in a bony socket of jaw bone is called :-

The ratio in which the plane vec r . (i-2j+3k) =17 divides the line joining the points -2i+4j+7k and 3i-5j+8k is

Evaluate : int(e^(2x))/(e^(x) + 2) dx

Find the number of 4 digited numbers that can be formed by using the digit 0,2,3,5,7,8 which are divisble by 2

A box contains 12 two rupee coins, 7 one rupee coins and 4 half rupee coins. If 3 coins are selected at random, find the probability that (i) sum of three coins is maximum (ii) each coin is of different value (iii) selection contains atleast one rupee coin (iv) all selected 3 coins have same value

Integrate the following functions (x^2+1)logx

Two vertices of an equilateral triangle are (0,0) and (3, sqrt(3)) then the third vertex can be